Starlings, brought to the United States from Europe in the late 1800's, are generally thought of as nuisance birds and, even worse, as health hazards.  They are also blamed for transferring diseases between livestock via bird droppings. 

Because of their similarity in species size and nesting habits, starlings are not only a nuisance, but a threat to woodpeckers as well.  Like the woodpecker, starlings nest in tree cavities (holes).  However, starlings are not able to create the hole or the nest, so they hang around while the woodpecker creates the nest and then they kick the woodpecker out of the nest it just created.  This process continues over and over again until the woodpecker either finds a suitable starling-free location or just gets lucky.

Another option is to install a woodpecker nesting box.  There are a variety of nesting box solutions out there, but the best seems to be one with an inward sloping face so non-clinging birds can not easily enter the nesting port.  The nesting box must also be protected from raccoons and squirrels via baffles, etc.  A project like this can reap great rewards if you enjoy having woodpeckers in your area.

Woodpecker-Feeder.com offers a suet feeding system that prevents all but the smartest of starlings from getting much suet at all.  The best those starlings can do is to launch themselves from a nearby location and briefly hover or hang long enough to make a stab or two at the feeder.  They get very little of the suet and look for easier food sources and this saves your valuable, quality suet for woodpeckers.  As the suet is eaten from each feeding port, less is visible to starlings, but woodpeckers can still find and eat the suet.  This way, your suet lasts longer and you have suet available when your woodpeckers and other clinging birds stop by.

Starling-resistant suet woodpecker feeders
Thoroughly researched and tested
Affordably priced